FLC OF A BRITISH JETSTREAM BA32 OVERSHOT ASSIGNED DEP ALT AND WAS NOT OBSERVED BY CREW UNTIL THEY HEARD THE ALT ALERT AT 1000 FT OVER ASSIGNED ALT.

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WE DEPARTED OVER 4 HRS PAST OUR SCHEDULED DEP TIME DUE TO SIGNIFICANT TSTMS IN THE AREA WHICH HAD FINALLY MOVED E OF OUR LOCATION AND ROUTING. WE WERE CLRED INITIALLY TO 3000 FT MSL ON A HDG 230 DEGS. ON CLBOUT WE WERE TOLD TO CONTACT DEP CTL. WE SWITCHED TO THEIR FREQ AND MONITORED THE CONGESTED RADIO TFC WHILE WE WAITED TO GET OUR CALL OUT TO THEM. AT THE SAME TIME WE WERE MONITORING A LARGE CELL ON OUR RADAR DIRECTLY IN OUR FLT PATH 5-10 MI AHEAD. BOTH OF US WERE FOCUSED ON THE TARGET CELL AND ADJUSTING THE RADAR'S TILT TO BETTER IDENT IT AS WE CLBED THROUGH OUR CLRNC ALT. NEITHER OF US CAUGHT THE ALT ALERT AURAL OR VISUAL ANNUNCIATION WITH OUR ATTN DIVERTED TO THE RADAR AND THE DENSE RADIO XMISSIONS DROWNING THE AURAL WARNING. THE CAPT WAS ABLE TO CONTACT DEP ABOUT THAT TIME AND DEP CLRED US ON UP TO 10000 FT MSL RIGHT ABOUT AS WE APCHED 4000 FT MSL. I THEN NOTICED THE ALT ALERT SOUND OFF AGAIN AT THE 1000 FT DIFFERENCE FROM SELECTED ALT. THE CAPT QUERIED ME ABOUT OUR ORIGINALLY CLRED ALT AND I CONFIRMED 3000 FT AND THE ERROR. THE REMAINDER OF THE FLT WAS UNEVENTFUL AND STANDARD. LESSONS LEARNED: 1) WHEN IN FMC; AT LEAST ONE HEAD SHOULD BE OUTSIDE THE COCKPIT AT ALL TIMES -- WE WERE LUCKY. 2) REGARDLESS OF RADIO SATURATION; RADAR IMAGES OR OTHER DISTRS; FLY THE PLANE FIRST! 3) DO NOT MISS STANDARD ALT CALLS (1000 FT PRIOR; 500 FT PRIOR). 4) BE MORE VIGILANT OF POTENTIAL PLTING ERRORS WHEN FLYING PAST NORMAL DUTY HRS INTO THE EARLY MORNING.